1. Field of the Invention
The present invention relates generally to active control apparatuses using adaptive digital filters, and more specifically, to an active control apparatus utilizing an adaptive digital filter for use in a signal control circuit used in an active noise cancellation apparatus, an active vibration control apparatus, an echo canceler, adaptive equivalent equipment and other active control systems.
2. Description of the Related Art
One example of an active noise control apparatus using an adaptive digital filter is shown in FIG. 11. In this apparatus, active cancellation of noise in a duct is conducted.
Referring to FIG. 11, a noise source 11 is present in a duct 12 having an opening at one end, and a microphone for detecting noise 13, a microphone for detecting noise cancellation error 14, and a speaker for noise cancellation 15 are disposed.
A noise detection signal xi(n) detected at noise detection microphone 13, then passed through an amplifier 22 and converted into a digital signal at an A/D converter 25 is added to the output v1(n) of a first adaptive FIR (Finite Impulse Response) digital filter 41 at an adder 42 to be a signal u1(n) , and is input into a second adaptive FIR digital filter 43. The output y1(n) of second digital filter 43 is output as a noise cancellation signal to a D/A converter 26. The noise cancellation signal converted into an analog signal at D/A converter 26 is output to noise cancellation speaker 15 through an amplifier 23. The output u1(n) of adder 42 is input to a first coefficient control portion 44 and an FIR digital filter for correction 45. Cancellation signal y1(n) is input to first adaptive digital filter 41 and first coefficient control portion 44. The output u11 (n) of correction digital filter 45 is input to a second coefficient control portion 46. The result of noise cancellation is detected at noise cancellation error detection microphone 14, and input as a noise cancellation error signal e1(n) to second coefficient control portion 46 through an amplifier 24 and an A/D converter 27.
The input-output relation of first adaptive digital filter 41 is given by the following equation (1): ##EQU1## where a1(i) is the filter coefficient of first adaptive digital filter 41, and M is the tap number of filter 41. (n) and (n-i) represent time.
Similarly, the input-output relation of second adaptive digital filter 44 is given by the following equation (2): ##EQU2## where b1(i) is the filter coefficient of second adaptive digital filter 43, and N is the tap number of filter 43. The filter coefficient a1(i) of first digital filter 41 is serially updated by the following coefficient updating formula (3) for the purpose of removing an acoustic feedback component detected at noise detection microphone 13 which has been created from sound output from noise cancellation speaker 15 and passed through duct 12. EQU a1(i,n+1)=a1(i,n)-.alpha.1.multidot.y1(N-i).multidot.u1(n) (3)
where .alpha.takes a small positive value in step size parameter. Updating filter coefficient a1(i) based on equation (3) provides a signal u1(n) with a component of noise detection signal x1(n) correlated with noise cancellation signal y1(n) being canceled. Accordingly, removal of the above-described feedback component can be achieved, contributing to suppression of howling and increase of noise cancellation effect. Coefficient updating based on equation (3) is performed at first coefficient control portion 44.
The filter coefficient b1(i) of second adaptive digital filter 43 is updated by the following equation (4), so that the mean electric power of error signal e1(n) is minimized. EQU b1(i,n+1)=b1(i,n)-.beta.1.multidot.u11(n-i).multidot.e1(n) (4)
where .beta.1 takes a small positive value in a step size parameter u11 (n) is produced by correcting the input signal u1(n) of second adaptive digital filter 43 using correction digital filter 45 and is given by the following equation (5). ##EQU3## where h1(i) is the filter coefficient of correction digital filter 45, and L is the tap number of filter 45. Correction digital filter 45 is characterized by a transfer coefficient from the output y1(n) of second digital filter 43 via noise cancellation error detection microphone 14 to second coefficient control portion 46. Coefficient updating based on equation (4) is performed at second coefficient control portion 46.
As a conventional technique, a digital filter having a previously calculated coefficient may be used in place of first adaptive FIR digital filter 41. At the time, the transfer characteristic of an acoustic feedback path from the output y1(n) of second adaptive FIR digital filter 43 via noise cancellation Speaker 15, and noise detection microphone 13 to the input u1(n) of second adaptive digital filter 43 is identified, and a filter coefficient for reproducing the characteristic is set.
In a conventional active noise control apparatus as illustrated in FIG. 11, if a noise waveform to be canceled is a random waveform, only acoustic feedback component can be canceled by updating the filter coefficient based on equation (3). Updating of the filter coefficient based on equation (3) however minimizes the mean electric power of signal u1(n) , and if a noise waveform is periodic, not only the acoustic feedback component but also the noise component itself is canceled. Accordingly, cancellation of resonant mode frequency in the duct cannot be performed. A conventional active noise control apparatus therefore cannot be applied to noise having a periodic element. This disadvantage is attributable to the fact that coefficient updating based on equation (3) is continued even if error signal e1(n) becomes 0, and the periodic component of signal u1(n) is canceled. Further, if a method of fixing the filter coefficient of first adaptive FIR digital filter 41 is employed, the transfer characteristic of the acoustic feedback path should be previously measured. This approach lacks adaption to change in external environment.
When duct noise cancellation is performed using an active noise cancellation system with the above described adaptive FIR digital filter without first adaptive FIR digital filter 41 in FIG. 11, the following disadvantage is also encountered. A sound wave output from noise cancellation speaker 15 propagates toward noise detection microphone 13, and therefore a standing wave is generated in the upstream of noise cancellation speaker 15. Assuming that the distance L1 between noise cancellation speaker 15 and noise detection microphone 13 and the wavelength .lambda.n of a sound wave are represented by the following equation: EQU .lambda.n=2/n.multidot.L1(n=1,2,. . . ) (6)
the node of the standing wave is at the position of noise detection microphone 13, the sound wave of wavelength .lambda.n cannot be detected, and therefore the sound of frequency cannot be canceled. This is illustrated in FIG. 12. In active noise cancellation utilizing FIR digital filters until today, a sound absorbing material is provided to the inner wall of a duct to reduce a standing wave ratio (SWR: amplitude ratio of node to antinode of standing wave), and the amount of acoustic feedback is restrained.
In order to overcome the above-described disadvantage, an IIR (Infinite Impulse Response) digital filter may be used in place of an FIR digital filter. A structure of an IIR digital filter 16 is schematically shown in FIG. 13. IIR digital filter 16 is formed of a non-recursive portion 18 and a recursive portion 17. If IIR digital filter 16 as such is employed for active noise cancellation, successful for updating of a filter coefficient adaptively could cancel some acoustic feedback by the function of recursive portion 17.
Now, the IIR digital filter will be described.
Generally, the transfer function H(z) of an adaptive IIR digital filter is given by the following equation (7): ##EQU4##
FIG. 14 illustrates a specific structure of such an adaptive IIR digital filter. The adaptive IIR digital filter includes a unit delay element 28, a multiplier 29, and an adder 30. An input signal u is applied to adder 30 through unit delay element 28 and multiplier 29, and is subject to addition at adder 30 to be output as an output signal y. a(i) and b(j) represent filter coefficients. Herein, an FIR digital filter portion formed of filter coefficient a (i) and implementing transfer function H.sub.N (z) given by the following equation (8) corresponds to the non-recursive portion 18 of adaptive FIR digital filter 16. ##EQU5##
The portion formed of filter coefficient b(j) and implementing a transfer function H.sub.R (z) given by the following equation (9) corresponds to recursive portion 17. ##EQU6##
For the input signal u(n) and output signal y(n) of adaptive IIR digital filter 16, the input-output relation is given by the following equation (10). ##EQU7## where N represents the tap number of non-recursive portion 18, while M the tap number of recursive portion 17. There are various kinds of updating algorithms for filter coefficients, one of which is to update a filter coefficient based on the following equations (11) and (12). EQU a(i,n+1)=a(i,n)+.alpha.u(n-1)e(n) (11) EQU b(j,n+1)=b(j,n)+.beta.y(n-j)e(n) (12)
where e(n) represents an output error d(n)-y(n) between a desired response d(n) and filter output y(n) , and .alpha. and .beta. represent step size parameter and takes a small positive value. Further, in order to increase the stability and convergence of filter coefficient updating, f(n) given by the following equation (13) may be used in place of e(n) in equations (11) and (12). ##EQU8## where c(l) represents the weight of a moving average, and is a predetermined constant. L2 represents the number of data over which the moving average is calculated.
Adaptive IIR digital filter 36 shown in FIG. 15 is the same as that in FIG. 14 with a filter coefficient updating control portion. Connection is made in non-recursive portion 18 so that input signal u(n) and output error signal e(n) are input to coefficient control portion 20 and control signals are input to respective multipliers 29 from coefficient control portion 20. Meanwhile, on the side of recursive portion 17, connection is made so that output signal y(n) and output error signal e(n) are input to coefficient control portion 21, and control signals are input to respective multipliers 29 from coefficient control portion 21. In the case of using equation (13) as well as in the cases of using the following equations (14) and (15) in place of u(n-i) of equation (11) and y(n-j) of equation (12), a structure basically the same as that shown in FIG. 15 is attained, and processing can be performed within coefficient control portions 20 and 21. ##EQU9##
FIG. 16 illustrates application of the above-described adaptive IIR digital filters 16, 36 to the processing portion of an active noise cancellation apparatus which suppresses noise, by radiating a sound wave having the same amplitude as and 180.degree. out of phase from the noise from a noise cancellation speaker, thereby causing sound wave interference. The content of FIG. 16 is basically the same as FIG. 11. A detection signal detected at noise detection microphone 13 is sent through preamplifier 22 to A/D converter 25 for analog-digital conversion, and the digitized signal is input to adaptive IIR digital filter 16. Input signal u(n) detected at noise detection microphone 13 is subject to an operation based on equation (10) at adaptive IIR digital filter 16, and the result of operation y(n) is output as a noise cancellation signal from noise cancellation speaker 15 through D/A converter 26 and power amplifier 23. The filter coefficient a(i) of the non-recursive portion 18 of adaptive IIR digital filter 16 and the filter coefficient b(j) of recursive portion 17 are serially updated at coefficient control portions 20 and 21 in response to a noise cancellation error signal -e(n) detected at noise cancellation error detection microphone 14 and based on signals input to respective coefficient control portions 20, 21 through preamplifier 24 and A/D converter 27. The detection signal detected at noise detection microphone 13 is input to coefficient control portion 20 through a digital filter 32 rather than through adaptive IIR digital filter 16, while the noise cancellation signal is input to coefficient control portion 21 directly from adaptive IIR digital filter 16 through a digital filter 31 rather than through noise cancellation error detection microphone 14.
Using equations (11) and (12), the updating formula is given by the following equations (16) and (17). EQU a(i,n+1)=a(i,n)+.alpha.u2(n-i) e(n) (16) EQU b(j,n+1)=b(j,n)+.beta.y2(n-j) e(n) (17)
u2(n) is produced by correcting the input signal u(n) of adaptive IIR digital filter 16 using digital filter 32, while y2(n) is produced by correcting the output signal y(n) of adaptive IIR digital filter 16 using digital filter 31. Digital filters 31 and 32 are characterized by the transfer characteristic from the output of adaptive IIR digital filter 16 via noise cancellation error detection microphone 14 to respective coefficient control portions 20 and 21.
Another conventional example is the one shown in FIG. 17 wherein desired response d is directly obtained. In this case, input signal u is subject to an operation at the non-recursive portion 18 and recursive portion 17 of adaptive IIR digital filter 16. The result of operation y is output as a noise cancellation signal, and the noise cancellation signal is compared to desired response d. A signal corresponding to noise cancellation error signal e is input to respective coefficient control portions 20 and 21. Output signal y is input to coefficient control portion 20 through recursive portion 17, input signal u is input to coefficient control portion 21 through recursive portion 17, and the filter coefficient of the non-recursive portion is updated. Thus, the u.sub.o (i,n) and Y.sub.o (j, n) of equations (14) and (15) are employed in place of u(n-i) and y(n-j) in equations (11) and (12).
In updating the filter coefficient of adaptive IIR digital 36 having recursive portion 17 as illustrated in FIG. 15, the instability and divergence of the filter can occur. The recursive portion 17 of adaptive IIR digital filter 36 sometimes suffers from divergence of its output in the course of updating the filter coefficient. In updating of the filter coefficient of recursive portion 17 is performed so as to minimize the level of the output of recursire portion or adaptive IIR digital filter 36 in parallel, a signal can be restrained from diverging at recursive portion 17, but if the input signal of adaptive IIR digital filter 36 is periodic and the periodic signal is necessary as the output of adaptive IIR digital filter 36, that necessary periodic signal is canceled at the recursive portion.
Furthermore, if equations (16) and (17) are used, the amount of calculation is increased. However, regardless of the amount of calculation, high speed operation is required. Application to active noise cancellation control requires operations at digital filters 31 and 32 as pre-processing of coefficient control portions 20 and 21, as illustrated in FIG. 16, naturally resulting in increase in the amount of calculation.